It’s never a good idea to wait until the last minute to get your graduate school applications together. Here is US New Education’s third installment of advice for completing your applications in a timely manner.

Many word problems seem to require us to write formulas in order to solve. Certain problems, though, qualify for a neat technique: Smart Numbers. We can actually pick our own real numbers and use them to solve!

* Lisa spends 3/8 of her monthly paycheck on rent and 5/12 on food. Her roommate, Carrie, who earns twice as much as Lisa, spends ¼ of her monthly paycheck on rent and ½ on food. If the two women decide to donate the remainder of their money to charity each month, what fraction of their combined monthly income will they donate? (Assume all income in question is after taxes.)

(No answer choices given; this is a fill-in-the-blank)

We’ve got two women, Lisa and Carrie, and they each spend a certain proportion of income on rent and on food. Annoyingly, the fractions don’t have the same denominators; even more annoyingly, the two women don’t make the same amount of money. All of that will make an algebraic solution challenging.

Here’s what an algebraic solution would look like. Let’s call Lisa’s income x. She spends (3/8)x on rent and (5/12)x on food. Add these together:

(3x/8) + (5x/12) = (9x/24) + (10x/24) = 19x/24

Subtract from 100%, or x:

24x/24 “ 19x/24 = 5x/24

Lisa donates 5/24 of x, her income, to charity. What about Carrie?

Carrie’s income is equal to 2x (because she makes twice as much as Lisa). How much does she spend on rent and food?Read more

Each week, we post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for two free Manhattan Prep GRE Strategy Guides.

Sn points are equally spaced on a circle, where n is an even number greater than 3. If 3 of the n points are to be chosen at random, what is the probability that a triangle having the 3 points chosen as vertices will be a right triangle?

Graduate school admissions committees will soon be making the decision whether to interview the applicants. As The Chronicle of Higher Education points out, the decision will depend greatly on the type of department to which the candidate has applied. Check out this article to find out which disciplines are more likely to invite candidates to interview.

*  A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 300 miles apart, at what time will the trains pass each other?

(A) 12:40pm

(B) 12:49pm

(C) 12:55pm

(D) 1:00pm

(E) 1:05pm

One of the strategies we discussed in the translation article was make the situation real. Put yourself into the situation and imagine you’re the one doing whatever the problem is describing. That will help you to set things up cleanly and correctly.

So what’s going on in this particular situation? First, you’re the conductor on the Kyoto train. At noon, you pull out of the station (instantly and magically traveling 240 miles per hour from the very start!). The track is 300 miles long; after one hour, where are you?

After one hour, it’s 1pm and you’ve gone 240 miles, so you’re just 300 “ 240 = 60 miles from Tokyo.

Okay, now switch jobs. You’re the Tokyo train conductor and you leave Tokyo at 12:10pm. After one hour, where are you? You’re going 160 miles an hour, so after 1 hour, it’s 1:10pm and you’re 300 “ 160 = 140 miles from Tokyo.

By 1:10p, have the two trains passed each other? Definitely, because train K (for Kyoto) is even further towards Tokyo at that point. Now, make a guess: do you think that the trains had already passed each other by 1p? Think about it before you read the next paragraph.Read more

After a difficult week on the east coast, we hope that those affected by Hurricane Sandy are making a fast recovery and that life is returning to as close to normal as possible. To help everyone ease back into the usual routine, we’ve complied our weekly list of grad-school related links:

Between deadlines, research projects, extracurricular activities, family commitments, and part time jobs, Graduate school can be extremely stressful. This week Grad Hacker shares some ways for grad students to combat stress and regenerate energy and interest in their work.Read more